How to integrate following governing equation for time range and x''g values?

I have to integrate the governing equation of a dynamic motion for given time interval and acceleration (x''g) to find the displacement (x).

Here's the equation

M*x"+C*x'+K*x = -r*M*x"g

M, C and K are nxn square matrices, x",x',x, and r are nx1 matrices and x"g is constant value availabe for time interval t1 to t2.

Solution of equation must provide value of x.

Kindly Help